Battery Internal Resistance Estimation Using a Battery Balancing System Based on Switched Capacitors

Battery management systems (BMSs) are key components in battery storage systems in order to guarantee their safe operation and improve their performance, reliability, and efficiency. BMSs monitor critical parameters in the battery as state of charge (SOC), state of health (SOH), or temperature. Direct measure of SOC or SOH is not possible, while temperature, on the other hand, can be measured with different types of sensors. These sensors, although cost-effective, raise concerns regarding cabling, signal conditioning and acquisition systems, increasing cost, complexity, and decreasing reliability. The internal resistor of the battery has already been successfully used to estimate these parameters. BMS can also include the function of balancing (equalizing) cells of a battery pack. Among all available equalizing systems, those based on switched capacitors are interesting due to their simplicity and easy scalability. This article proposes an internal resistance (IR) estimation method for LiFePO4 batteries using signals naturally produced by a switched-capacitor equalizer (SCE). The IR will be used to estimate the battery temperature. It will be shown that the method can operate online and without interfering with the regular operation of the SCE.

in a broad range of applications, such as electric vehicles [2], smart grids [3], aerospace applications [4], and all kinds of small appliances applications as mobile devices [5].
There is a wide variety of rechargeable battery (secondary batteries) technologies that could be used for ESS, as nickelcadmium (NiCd), Pb-acid, or lithium-ion (Li-ion). Among these, Li-ion batteries (LIBs) are one of the most appealing batteries for high-capacity ESS due to their high energy density, good temperature operation range, low self-discharge, high efficiency, and high cell voltage compared with NiCd or Pb-acid [5], [6].
Since the cell voltage and/or current in any of these cases is low compared with typical industrial requirements, battery packs are built stacking cells in series and/or parallel configurations [2], [6]. Manufacturing tolerances, temperature differences, cell distribution inside the pack (which affects the battery temperature), among other reasons, result in voltage imbalances among cells during normal pack operation. These imbalances accelerate the aging of cells and result in an increase of the internal battery resistance and a decrease in its capacity. Mismatches in voltage among cells also increase the internal battery temperature, decreasing, therefore, operation safety [7], [8]. Thermal behavior is also heavily affected by how the battery is employed in terms of current demand and sudden load changes [9]. Active materials in the LIBs can be potentially damaged in the case of overvoltage or undervoltage [10], [11]. For all these reasons, battery management systems (BMS) are needed to increase the overall safety of the system: monitor critical parameters as temperature, state of charge (SOC) or state of health (SOH) [3]- [13], control operational conditions and cell balancing, extend the life of the battery and ensure a safe range of operation for all the cells forming the pack [6], [12].
One of the main features of BMSs is the equalizing of cells, which allows us to maximize the energy extracted from the battery pack without compromising safety [11]. Among proposed equalizers in the literature, the SCEs [11], [14]- [18] are one of the most appealing techniques to equalize single cells due to its low cost and simplicity. They can be used to balance all kinds of battery chemistries, as Pb-acid or nickel-based [14] or LIBs [11], [17], [18]. Unlike other equalizers, SCEs can work effectively both during battery charging or discharging [7]. SCEs equalize cells in terms of voltage, which means that there will be energy transfer between the cells while there is a voltage difference among them.
Another important feature of a BMS is battery temperature knowledge. Batteries' temperature can be directly measured using temperature sensors [19]. These sensors, although cheap, raise concerns regarding cabling, signal conditioning and acquisition systems, increasing cost, system complexity, and the number of elements susceptible to failure [20], [21]. As an alternative, the batteries' temperature can be estimated. Temperature estimation methods based on the dependency of a battery parameter with its temperature are the most popular [19]- [23]. On the other hand, since SOC and SOH cannot be directly measured, estimation methods must be implemented [12].
Several methods to estimate battery parameters can be found in the literature: the real part [19], [21], the imaginary part [20], the magnitude [21], and the phase shift [23] of the battery impedance being the most relevant. This kind of methods estimate the battery impedance from the battery terminal voltages and currents when the battery is being connected to a power converter that has the capability of injecting some high-frequency signal superimposed on top of the fundamental dc component, i.e., these methods work in an analogous way to the electrochemical impedance spectroscopy (EIS) analysis [20] but only for a single frequency.
This article, which is the extended version of the conference paper [1], proposes an online battery internal resistance (IR) [24] estimation method, i.e., during cell balancing, for SCEs. The IR of the battery is estimated using signals produced by the SCE regular operation; the IR will be used for cell temperature estimation, therefore this method cannot be directly compared to [19]- [23]. Nevertheless, and since battery packs can be connected to the rest of the system using a power converter, both estimation methods could be employed simultaneously, thus increasing the reliability of the temperature estimation. Besides, and as it will further explained in Section IV, once the cells are equalized, there is no voltage difference among them, nor equalization current, meaning that the IR can no longer be estimated with the proposed method. Due to this, combining the proposed method in this article with the ones proposed in [19]- [23], in those cases where a power converter is employed to connect the battery pack to the rest of the system, could be a way of expanding the cell temperature estimation. The current level and SOC could also affect the proposed method, this will be analyzed in Section IV.
The article is organized as follows: the basis of SCEs is presented in Section II; electrical modeling of batteries is discussed in Section III; the proposed method for battery IR estimation is presented in Section IV; simulations and experimental results are shown in Sections V and VI, respectively; conclusions are finally presented in Section VII.

II. SWITCHED-CAPACITOR EQUALIZER
This section presents a brief review of different equalizing methodologies, focusing on switched-capacitor equalizers (SCEs). Battery/cell equalizers extract energy from the most charged cell of a battery pack and either dissipate or transfer it to a less-charged cell. The first method is known as passive balancing and the second as active balancing. Passive balancing is relatively inexpensive and easy to implement, although dissipating excessive energy makes it inefficient. Due to this, recent research efforts are focused on active balancing methods. Methods for active balancing can be classified according to different criteria, as the connections between the cells (cell-to-cell, pack-to-cell, cell-to-pack …) or according to the circuit topology (shunting, shuttling, or energy conversion methods) [7], [12]. Shunting methods transfer the energy from one cell to another without any external energy storage device, unlike shuttling methods that use external energy storage devices, e.g., capacitors, inductors, or other batteries. The so-called energy conversion methods [7] use isolated converters for equalizing the cells. This solution is the most expensive among them and often used to balance packs of cells, while the other two are more suitable to equalize single cells.
Among shuttling active balancing methods, one of the most appealing methods to equalize single cells is the switched capacitor equalizer [14], due to its low cost and simplicity. This cell-to-cell equalizer balances the voltage of N cells with N-1 capacitors and 2N switches, see Fig. 1(a). The switches continuously work during regular operation of the battery with a fixed duty cycle of 50% but the corresponding dead time to avoid shortcircuit, alternating ON/OFF states between switches "a" and "b." This results in a very easy system that can work without any control strategy: there will be energy transfer between the cells if there is a voltage difference among them. This can be seen in Fig. 1(b), where Ts is the switching period and dt is the dead time. This way, each capacitor is connected half of the switching period in parallel with one cell and the second half with an adjacent cell, transferring energy from the one with the highest voltage to the one with the lowest voltage. This is schematically shown in Fig. 1(c) assuming VB1 > VB2 > VB3. In the state 1 (in red), B1 charges C 12 and B2 charges C 23 , i.e., they are connected in parallel, and in state 2 (blue), C 12 discharges over B2 and C 23 discharges over B3.
The main advantages of this equalizer are that it does not require control, it is fully scalable, cost-effective, and easy to implement. In addition, and unlike other methods, it can work effectively both in charge and discharge [7]. As a drawback, cells only transfer energy effectively to their adjacent ones, so the energy might need to flow through a large number of cells, which increases the losses and the equalization time [11]. Another drawback is that the equalization speed depends on the voltage difference, so the process becomes slower as the voltage difference decreases. Note that this equalizer may induce losses if the switching is maintained once the cells are voltage balanced. To avoid this, a voltage threshold to start and stop the equalization may be selected. Since SCEs can be used with different types of battery chemistry [14], the selection of this threshold will depend both on the application and the cells that are being balanced. For example, when equalizing lead-acid cells, the threshold can be higher than when equalizing LiFePO 4, since the latter has a much flatter SOC-OCV curve [12]. This threshold will also be related to the resolution of the acquisition system, as will be explained in Section VI. It can be concluded that it is not straightforward to give a threshold figure valid for any battery chemistry/application.  A prototype for an SCE to balance four cells is shown in Fig. 1(d). This prototype will be used for the experimental verification of the proposed battery IR estimation method.
The SCE from Fig. 1(a) can have large equalization time, especially if the capacity of the cells is high or they are extremely unbalanced. However, it is expected that this time is reduced if the SCE is permanently connected since it will not allow large unbalances among cells. To reduce this time, different SCE topologies have been proposed. These equalizers improve the equalization time at the price of increasing the number of components used or the loss of modularity. These alternative SCE topologies are briefly analyzed in the following paragraphs [11], [14]- [18].

A. SCE Topologies
1) Basic SCE [14]: Fig. 1. Explained earlier in this section. 2) Double-tiered SCE [11], [15], [16]: Fig. 2. An extra capacitor bridges the capacitors in the first row, so batteries have two paths to exchange charge, reducing the equalization time. As a drawback, there is a need for adding an extra capacitor to the system, which must withstand the combined voltage of all the capacitors, compromising the scalability of the topology.
3) Chain structure using additional switches or capacitors [11]: Fig. 3. Requires four additional switches compared to the double-tiered SCE, top and bottom cells become, therefore, adjacent, forcing them to exchange energy between them and their adjacent cells only, and not with all the cells in the pack as in the previous case. The scalability of this topology is compromised as in the previous case since the voltage that the new switches must withstand is the same as the whole battery pack.
4) Star-structured SCE [15]: Fig. 4 left. It requires one additional capacitor respect to the classic proposal and connects the capacitors in a star-structure that allows the interconnection of all the cells at the same time, which decreases the equalization time (making it independent of the initial imbalance status of the string) and efficiency. As a drawback, the scalability is  again compromised because the voltage that each capacitor must withstand is different. A variation of this equalizer with one less capacitor can be seen in Fig. 4 right, [15], [17]. 5) Delta-structured SCE [18]: Fig. 5. This equalizer adds capacitors in such a way that there is always one capacitor connecting any two cells, allowing the interconnection of all the cells at the same time. As the double-tiered SCE, it maintains the number of switches but increases the number of capacitors (in a higher number) while reducing the equalization time. The voltage that each capacitor must hold is different and dependent on the cells they are bridging.
A summary of the SCEs presented in this section is given in Table I  The previous discussion considered only balancing systems based on switched capacitors. They all have, in common, the same working principle, being cost-effective solutions easy to implement, thanks to the absence of control. The main difference among them is the number of components and their connection, which changes the equalization time. There are more complex systems based on the same principle that combine inductors and capacitors to improve the performance in terms of speed and losses, such as achieving zero-current switching [25]. However, the increased difficulty in the design and number of components makes them impractical for low-cost applications.
The Randles model [ Fig. 6(a)] is obtained from the EIS, a standard methodology for battery characterization. It consists of applying ac voltage to the battery and measures the resulting current to estimate the impedance at different frequencies [ Fig. 6(b)] [27], [28]. Each range of frequencies is dominated by different phenomena in the battery [diffusion effect, solid-electrolyte interface (SEI) resistance, metal collectors, etc.] [20].  Fig. 6(a), Z w represents the Warburg impedance, which accounts for the diffusion phenomena (low frequencies). The RC circuit corresponds to the electrolyte and SEI resistance on the anode. Finally, R i is the IR, point in Fig. 6(b) when the battery impedance changes from capacitive to inductive [20], [27]. Fig. 6(b) shows the EIS analysis (Nyquist plot) of the LiFePO 4 cell used in this article; the x-axis represents the resistance and the y-axis represents the reactance (sign reversed), while each point in the graph corresponds to a different frequency. The frequency increases following the arrow direction where the red point indicates the smallest analyzed frequency.
On the other hand, the Thèvenin model, see Fig. 7(a), can be obtained from the battery response to a current step; parameter identification is obtained from the voltage transient response, see Fig. 7(b) [29]. In Fig. 7(b), R i is the cell IR, accounting for the resistance of the contacts, terminals, collectors, electrodes, and electrolyte, while R D and C D model the dynamic response, resulting from the effect of diffusion and charge transportation. Finally, C SOC models the battery capacity, C SOC voltage representing the battery open-circuit voltage (OCV) [26], [30].
The transfer function of this model is shown in (1). The first term on the right-hand side of (1) corresponds to the IR, R i , and is obtained from the initial response to the current step, see Fig. 7(b). The second term on the right-hand side of (1) is the dynamic RC circuit, a first-order system corresponding to the exponential part of the voltage variation, see Fig. 7(b). The last term on the right-hand side of (1) is C SOC , a pole at the origin, which accounts for the continuously increasing slope in the voltage in Fig. 7(b) due to a constant current.
Among these models, the Thèvenin one is the most appropriate for battery parameter identification using an SC equalizer, since the process for extracting the parameters involved in (1) (i.e., step response) is similar to the steps produced in the battery as a result of the SC switching.

IV. BATTERY PARAMETER IDENTIFICATION BASED ON SC EQUALIZERS
This section presents the proposed method for battery IR estimation using signals produced by the SCE operation. A simplified scheme of an SCE is presented in Fig. 8(a), where the battery and SCE parameters are shown in Table II. The circuit is connected at the instant t i , and the waveforms resulting from this connection are shown in Fig. 8(b), which resemble SCE waveforms. Note that applying an impulse in the voltage is analogous to applying an impulse in the current from the point of view of battery parameter estimation [29].
Before the switch connection, there is no current circulation, so the voltage measured [V bat in Fig. 8(a)] is the OCV (the voltage in the capacitor C SOC ). After the switch connection, there is a current flowing from/to the battery and consequently a voltage drop in the battery IR, R i , exists. Therefore, R i can be obtained from (2). V bat (t i +) and I bat (t i +) are the voltage and current right after the connection instant (t i ), see Fig. 8 Fig. 8 When using this SCE, two different currents may be superimposed, the current through the series-connected cells due to the charge/discharge of the battery and the transient current due to the switching of the SCE. The first current, which will be dc, can be controlled provided that the battery is connected to a power converter. The second current cannot be controlled since it depends on the voltage difference between the cells been equalized. As seen in [21], the current level may affect slightly the IR estimation. This effect can be compensated using an analogous procedure as shown in [21], using a look-up table to decouple the current level effect on the estimation.
The IR measured in batteries can change depending on the frequency of the signal used for measurement. The IR measured using the proposed procedure is a high-frequency resistance since the transient response of the battery is used for the estimation. At high frequencies, the IR is dominated by the leads and metal collectors of the battery [30]. Due to this, SOC is not expected to affect the estimation, since it does not affect the high-frequency impedance on LIBs [21], [23]. SCEs can effectively work both during the charge and discharge of the cell [7]. In case the battery is being charged or discharged, the method is similarly applied with the exception of the current in Fig. 8(b) will include this charging/discharging current. In this case, a more general equation, (3) should be used. I bat (t i ) is the current before the commutation, in this case, the current been charging/discharging the battery. The absolute value allows, as in (2), the equation to be used for both charging and discharging. The results remain unchanged.
The limitations of the method can be extracted directly from (3): once the batteries are equalized, there is no voltage difference among them, nor equalization current, meaning that R i cannot be estimated this way. The SCE used in this article (see Fig. 1) equalizes based on voltage differences among cells, however, LiFePO 4 cells can have a rather flat OCV-SOC curve [12], so it may not achieve a perfect balance in terms of SOC. This is a limitation of the SCE employed in this article. Nevertheless, this SCE can be used with any LIB technology with less flatness OCV-SOC [12]. Besides, and as stated in the introduction, this method can be combined with signal-injection based battery resistance estimation methods to estimate temperature. This would increase the reliability of the estimation, allowing to estimate the desired parameters even when the method proposed in this article cannot be employed.

A. Effect of Inductive Parasitic Components
As will be seen in Section V, the circuitry has some unavoidable parasitic inductances due to, e.g., cabling that affect the waveforms shown in Fig. 8(b). This effect can be simulated by adding a small inductor (an inductor of 0.1 nH has been used to emulate this effect) in series with C EQ in Fig. 8(a). The resulting waveforms are shown in Fig. 9. The orange waveform represents the response of the battery's voltage and current when the inductor is added to the circuit, in comparison with the blue waveforms that show the ideal case.
Since V bat is measured at the battery terminals, the existence of this parasitic inductor does not affect the estimation of the IR.
Any combination of voltage and current from the graph would result in the IR estimation. However, peak values are preferred since they provide a high signal-to-noise ratio. Equation (3) can be rewritten as (4), where V batpeak and I batpeak correspond to the peak values for current and voltage, respectively, right after t i .
V batpeak and I batpeak can be obtained from the derivatives of V bat and I bat , respectively, which can be approximated by (5) using the Euler approximation, where X bat represents either the current or the voltage, X´b at represents either the discrete-time derivative of the current or the voltage, k represents the current time instant, and T s is the sampling time. V batpeak and I batpeak are theoretically acquired when X´b at is zero; in practice, when there is a change in the sign of X´b at .

B. Battery Temperature Estimation
It is generally expected [13], [20], [23] that the battery resistance decreases as temperature increases at low frequencies. In this region, the electrolyte and SEI dominate the behavior of the battery and follows the Arrhenius law [20]. However, it must be noted that the proposed method estimates the IR, R i in Fig. 8, which is dominated by the metal collectors and leads [30], which resistances increase as the temperature does [13], [23]. Hence, IR can be modeled as a linear function of the battery temperature (6), provided that the metallic part of the battery dominates the response. R bat0 is the battery resistance (R i ) at the room temperature (T o ), T bat is the battery temperature and α bat is the temperature coefficient; R batn0 and α bat can be measured during a commissioning process. The battery temperature is finally estimated from (7).
It is finally noted that although the method proposed in this article is evaluated for the classical topology, see Fig. 1(a), it can be extended to any other switched-capacitor topology, see Section II-A.
V. SIMULATIONS An SCE with two cells was implemented in MAT-LAB/Simulink, see Fig. 10.
The equalizer main parameters are shown in Table III. Cells are implemented using the battery model from Simscape Electrical toolbox, with LiFePO 4 battery equivalent parameters. A 30% difference in SOC between cells is set as the initial condition: the most charged battery has an OCV of 3.312 V and the less charged one has an OCV of 3.284 V. Fig. 11(a) shows the voltage and current of the most charged cell (B1 in Fig. 10) when it is connected in parallel to the balancing capacitor at t = 5 μs. Voltage and current waveforms  are seen to be in good agreement with the ones obtained with the Thèvenin model, see Fig. 8(b). The estimated IR (2) is ≈50 mΩ, which matches R i defined in Table III and included in the cell model for the simulation. The same results are obtained if the parasitic inductor is added in series with C eq [ Fig. 11(b)], as it was explained in Section IV-A.
Simulation results with more than two cells have also been carried out. A simulation scenario with three cells (ideal case), see Fig. 1(a), has been used, voltage and current are measured for B2, since this cell will share energy with both the upper (B1) and lower (B3) cells. SOCs of B1, B2, and B3 are 80%, 50% and 20% respectively. The resulting waveforms for a switching cycle (voltage ad current) can be seen in Fig. 12.
As expected, in the first half of the switching cycle B2 charges the bottom capacitor (C 23 ) since its voltage is higher than the one from B3. In the second half of the switching cycle, B2 receives energy from the upper capacitor (C 12 ), since B1 has a higher voltage than B2. The cell IR can be calculated from any of these two transient responses with identical results. Different SOCs and arrangement of the cells would not interfere with the method either.

VI. EXPERIMENTAL RESULTS
The SCE shown in Fig. 1(c) was used to carry out the experimental results. A two-cell arrangement has been used to be consistent with the simulation results shown in Section V. Current and voltage waveforms were measured with a Yokogawa 701932 current probe and with a Yokogawa 701938 voltage probe, respectively. Signals were captured with a Yokogawa 720250 12-bit 2-channel module plugged into a Yokogawa DL850 ScopeCoder. Parameters of the cell and SCE are shown in Table II.   Fig. 1(a)]. Table III, the equivalent series resistance of the equalization capacitor is 0.7 Ω [31]. This resistance will affect several aspects of the system: 1) it affects the equalization time and the efficiency of the equalization [11]; 2) it will affect the sensitivity of the method, i.e., the bigger this resistance, the smaller will be the current peak and the highest the accuracy needed in the measurement system. It is also noted that the ON resistance of the MOSFETs will affect in a similar way; the ON resistance of the selected MOSFET is 2.4 mΩ [32]. In general, when designing an SCE, and since they are intended for low-cost applications, a good compromise among parasitic resistances, the overall performance of the components and cost must be achieved.  The LiFePO 4 cell used in this article is shown in Fig. 13(a). Voltage measurement is performed at cell terminals. Cell voltage and current in one switching cycle are shown in Fig. 14. It can be seen that the current has a smoother response than in the ideal simulation [ Fig. 11(a)], and similar to Fig. 11(b), due to inductive parasitic components present in the actual system, as it was previously explained in Section IV-A, hence (4) is used to estimate the IR.

In addition to the parameters shown in
The OCV-SOC curve of LiFePO 4 batteries is rather flat [see Fig. 13(b)] [12], meaning that the accuracy of the measurement system should be carefully analyzed. As stated in [12], a good target for SOC and IR estimation in these batteries would be in the range of 1-2 mV. The least significant bit (LSB) indicates the resolution of an acquisition system and is the result of dividing the full-scale range of the acquisition system by the number of discrete values obtained with n bits (8) [33]. With a 12-bits resolution acquisition system, which is a common resolution in digital processors nowadays (e.g., DSPs), the LSB would be < 1 mV, which is in the recommended range in [12].
Besides, the method does not work when the cells are equalized within the LSB limit, see Section IV. The LSB would be, then, the minimum threshold below where the proposed method would not work. In practice, this value will increases due to unavoidable noise in the real signals, as can be appreciated in Fig. 14. This methodology could be used with any LIB chemistries (not only in LiFePO 4 batteries which have the flattest profile among LIBs) [14]. It is finally noted that the voltage variation is expected to be always smaller than the current variation, so the current variation will not be a problem before the voltage variation is.

A. Resistance Variation With Switching Frequency
Switching frequency in an SCE can be optimized for a given capacity of the equalizing capacitors [34], in such a way that the capacitor can be fully charged/discharged during its switching cycle without staying charged/discharged for long before the next commutation. The maximum equalization frequency is related to the driver (driving the MOSFETs). In addition, increasing the switching frequency allows for a capacitor size reduction, but it also increases the switching losses in the MOSFETs, thus reducing the efficiency. In the case of the setup used in this article [see Fig. 1(d)], the maximum switching frequency is ≈ 50 kHz. Fig. 15 shows the estimated cell resistance for a set of experimental data captured with the SCE working at 10, 20 , and 30 kHz; the mean value of the estimated cell resistance is shown in red.
The mean value at all the frequencies of the estimated resistances shown in Fig. 15 is similar at all the frequencies since   the resistance being estimated is R i , which depends on the voltage/current at the switching instant, which is independent of the SCE switching frequency. It is also noted that SOC, SOH, or temperature-time constants are significantly larger than battery resistance estimation time [35], meaning that averaging the measurements for a certain period could be an acceptable and easy solution to reject measurement noise. Experimental results are repeated with another cell (see Fig. 16) with the same characteristics, to show the replicability of the methodology. It is shown that the R i mean value is independent of the switching frequency. However, the absolute value of R i is different: for the first cell the mean value of R i is ≈ 40 mΩ, while for the second one is ≈ 30 mΩ. This was expected due to differences among cells existing in practice [7], [8]. Temperature   Fig. 17 shows the estimated IR for three different cells as the temperature increases. The cells are slowly heated (for around 45 min, see Fig. 18) up to 65°C while capturing current, voltage, and temperature. The temperature of the cells is monitored using LM35 temperature sensors [36], placed on the surface of the cell. It can be observed from Fig. 17 how the cell resistance increases almost linearly with temperature for all tested cells.

B. Resistance Variation With
It can be observed from Fig. 17 that, although there is an offset among IRs, the rate of variation of IR with temperature is similar for all cells under test. Offsets present among cells will not affect the accuracy of the proposed method because the cell temperature will be estimated from variations of the resistance with temperature respect to the room temperature resistance (R bat0 ) as seen in (7). Fig. 19 shows the measured and estimated temperature using (7). First, the slope that best fits the temperature variation for each of the three cells was obtained (see Table IV), then, the average value of this slope (α bat = 16.72 1/°C) is used to estimate the temperature for all cells under test. The temperature estimation error for the three cells analyzed is shown in Fig. 20; the temperature estimation error is seen to be less than ≈ 12°C for any point, with a mean value of 4°C and a standard deviation of 4.11°C. Due to this difference, it is important to analyze more than one point every time, as seen in Figs. 15 and 16, so the conclusions in terms of temperature are valid.

VII. CONCLUSION
This article proposes the use of signals naturally produced by SCEs to estimate the battery IR. The method operates without interfering with the regular operation of both the equalizer and battery and is valid for a wide range of switching frequencies.
The IR estimate can be used to obtain the battery's temperature. However, its main limitation is that once the cells are equalized the IR cannot be estimated. Experimental results have been provided to demonstrate the viability of the proposed method. He joined different technical companies. In 2005, he joined Electrotécnica Industrial y Naval as R&D Manager. He has been participating in several R&D projects for industry, navy, and energy such as smartgrids, power converters, and energy management. He has also supervised several M.Sc. and Ph.D. thesis. He has published more than 15 scientific papers. His current research interests include new converters topologies and uses and power converters manufacturing.
Dr. Pereda is currently a Member of Editorial Board for Dinamo Técnica magazine. He was the recipient of nine IEEE Industry Applications Society Conference and IEEE Energy Conversion Congress and Exposition prize paper awards. His research interests include sensorless control of induction motors, permanent magnet synchronous motors, and digital signal processing.